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传统的求解函数高阶导数值的方法就是先求出高阶导数的函数表达式,然后将自变量值代入,就得到了此点的高阶导数值。高阶导数的函数表达式的推导比较的烦琐,尤其对于复合函数来说。利用改进的遗传算法和神经网络各自的优点,提出求解函数高阶导数值的GA-Network法。算法采用多目标优化的思想,使用“动态自适应策略”和“罚函数法”。利用神经网络来构造函数泰勒展式的网络结构,用遗传算法对网络进行学习,最后得到网络的输出结果即高阶导数值。通过对初等函数的仿真实验,可以看出此方法有比较高的精度,它也为函数导数值的求解提供了一种方法。
The traditional method of solving the high-order derivative of the function is to find the function expression of the high-order derivative first, and then the independent variable value is substituted into the high-order derivative value of this point. The derivation of function expressions for higher-order derivatives is cumbersome, especially for complex functions. By using the respective advantages of improved genetic algorithm and neural network, a GA-Network method is proposed to solve the high-order derivative of the function. The algorithm uses the idea of multi-objective optimization, using “dynamic adaptive strategy” and “penalty function method.” Using neural network to construct the Taylor-style network structure of function, using genetic algorithm to study the network, and finally get the output result of the network, ie, high-order derivative value. Through the simulation experiment of the elementary function, we can see that this method has higher accuracy, and it also provides a method for solving the function derivative value.